The first GraWIToN school offered me at least three of the many benefits that comes from doing a PhD: learn new things, see new places, and meet interesting people.

The modules of the school covered the subjects that make up the field of gravitational waves, and were all good and relevant, together providing a broad overview of the field. All the lecturers were well prepared and engaging, and the food in the canteen was great, as well as the snacks at the coffee breaks. Overall, the school was very well planned and organised.

I definitely enjoyed my first visit to Pisa and Italy. Eating tasty Italian food, walking around on the narrow streets, and hanging out by the river or at some square among all the uncountable students are definitely things I could do more of. It was fun to finally see and walk up the famous leaning tower, but to me, the by far coolest sight was the VIRGO observatory.

All of the above things became even more fun when doing it together with the fun group of people that participated in the school. Meeting all these people, as well as the teachers and the organisers of the school, made me feel as a part of the gravitational wave community, which is a feeling I find very motivating. However, some evenings my focus on "networking" may have been a bit too high compared to my focus on getting enough sleep, but it was worth it! I am definitely looking forward to meet everybody again, either at a future GraWIToN school or at some conference.

The last month I have started to look into the problem of finding good, or possibly, the best values for the degrees of freedom of an interferometer. Such set of values is called an operating point. So far, I only consider a single Fabry-Perot cavity, that is, two mirrors facing each other. In this case the only degree of freedom is the cavity length, which can be controlled and kept close to the operating point by using a feedback loop. For this we use an error signal (see fig. 1) that is approximately linear around the operating point, thus, the length deviation can be determined by observing how the error signal differs from its operating point value. Without noise, the operating point is preferably chosen to be at a resonance peak (see fig. 1), which also coincides with the zero crossing of the error signal. Thus, the sign of the error signal determines if the cavity length has increased or decreased. However, when noise is introduced, it is also important to keep the coupling of the noise into the error signal as low as possible. Now we have three possible criterions for the operating point: the resonance peak that yields maximum circulating power, the zero crossing of the error signal used to control the cavity length, and the minimum coupling of noise into the error signal. Unfortunately, when noise and optical defects are introduced to the system, these three points do not generally coincide.

I am currently investigating how much these three points deviate from each other while letting the laser power fluctuate and allowing different degrees of some types of imperfections, e.g., misaligned cavities and mirror surface defects. Figure 1 shows the resonance peak, the error signal and the coupling of the laser power noise into the error signal. The cavity is slightly misaligned, but in this case not enough for us to see (without zooming further) any splitting of the three red lines marking the three criterions mentioned above.

To perform these calculations the laser interferometry simulation package FINESSE is used, in which the laser beams are constructed by summing transverse electromagnetic modes (TEMs). The larger and more complex imperfections that are introduced, the more modes need to be included in the sum, which naturally makes the calculations slower. It is important to use enough TEMs to make the calculations correct, while also trying to not use way too many modes since this significantly slows down the machinery. This led me to spend time looking for a relation between the degree of an imperfection and the number of TEMs needed. Figure 2 shows how many TEMs that are needed for the circulating power to converge for a few different misalignment angles of the input mirror of the cavity.

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